[TowerTalk] Feedpoint Impedance

jimlux jimlux at earthlink.net
Tue Jul 29 13:58:23 EDT 2008

Ward Silver wrote:
>>>> Radiation resistance should be fixed..
>>> Oh, right...duh.
>>> The current equation will do - but the radiator (I may have confused 
>>> things by referring to it as a "dipole") may be anywhere between one-half 
>>> and one wavelength long, so the current won't be a simple cosine 
>>> function.  It *will* be zero at the ends :-)
>> I think Orfanidis's book has the equation you're looking for.. actually 
>> several approximations, of varying fidelity..
>> I'm pretty sure there's some standard assumptions of the current 
>> distribution shape (ranging from uniform for very short, to triangular to 
>> sinusoidal to something else), possibly broken up into segments.
>> What sort of accuracy are you looking for?
> 20% ought to do it.  There will be significant variation depending on 
> proximity of ground, type of ground, and so forth.  At this point, I'm just 
> doing a feasibility study.
> 73, Ward N0AX 
Here you go...

Current on a thin wire of length 2*h
k is propagation constant (i.e. pi gives you a half wavelength dipole)
z is the distance from the center
I(0) is the current at the center

I(z) = I(0) * sin( k *(h-abs(z)))/sin(k*h)

(Eq 21.4.2 from Orfanidis's book)

Seems to match (by eye) what I got from a series of NEC models..

I haven't looked into the off center fed aspect...This is just the 
current distribution on a center fed wire.

Later pages in Chapter 21 of the book talk about King's three term 
approximation (which works up to about 1.25 lambda).  Figure 21.6.1 
shows a comparison between sinusoidal, King and numerical integration.

If you want real pain, he goes on to work out an exact kernel for the 
solution of Pocklington's equation using, why yes, elliptic integrals.

(I'd just use his canned Matlab routines....)

Jim, W6RMK

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